This paper evaluates the steady-state tracking performance of the soft DTTL symbol synchronizer which is a low SNR approximation of the hyperbolic tangent nonlinearity in the in-phase channel. The normalized s-curve, slope of the s-curve, and normalized noise density are derived and compared to the hard DTTL which is a high SNR approximation of the nonlinearity. Moreover, the symbol SNR region where the steady-state timing jitter of the soft DTTL outperforms that of the hard DTTL is determined.

When signals from a user (fixed or mobile) are received at multiple antennas, the signals can be arrayed to increase the signal-to-noise ratio (SNR) of the received signal. This article describes two maximal ratio combining techniques referred to as full spectrum combining (FSC) and complex symbol combining (CSC), and then compares them in terms of the achievable arraying gain. Although the performance of these techniques is derived for the case of binary phase shift keying (BPSK) signalling in an additive white Gaussian noise channel, the analytical techniques here are applicable to other modulations and channels. The paper also addresses the use of symbol SNR degradation and symbol SNR loss as system performance measures. It is shown that degradation and loss are equal at weak signal levels but degradation is a lower bound for loss when the signal is strong. The telemetry arraying techniques described are applicable to any phase modulated signal. We assess the deep space communication channel performance scenario where the weakest signals ever are detected.

This paper describes the performance of the all digital data transition tracking loop (DTTL) with coherent and noncoherent sampling using nonlinear theory. The effects of few samples per symbol and of non-commensurate sampling and symbol rates are addressed and analyzed for perfectly square pulses as well as filtered pulses. Their impact on the probability density and variance of the phase error are quantified through computer simulations. It is shown that the performance of the all-digital DTTL approaches its analog counterpart when the sampling and symbol rates are noncommensurate (i.e., the number of samples per symbol is irrational). The phase error variance for an even number of samples per symbol is also shown to degrade compared to an odd number of samples per symbol.>